I know there is a "formal proof" in "natural deduction" for the "rule of absorption" that employs the "law of excluded middle". It is presented in Wikipedia (and I think it is Russell's): https://en.wikipedia.org/wiki/Absorption_(logic)#Formal_proof.
It is also obvious how the proof could be done by way of a "conditional" or "indirect" proof.
However, is there a "formal proof" in "natural deduction" for the "rule of absorption" that does NOT assert the "law of excluded middle (or non-contradiction)" as a rule of inference or employ a "conditional (or indirect) proof"?
That is to say, can a proof in "natural deduction" be constructed that goes from the premise p⊃q to the conclusion p⊃(p∙q) WITHOUT using the "law of excluded middle (LEM)" as a rule of inference or employing a "conditional proof (CP)" or "indirect proof (IP)"?
